Method for processing a distortion-corrected 2D or 3D reconstruction image recorded by a magnetic resonance device

ABSTRACT

In one embodiment a method for processing a reconstruction image is disclosed. The method includes recording the reconstruction image by a magnetic resonance device having a gradient coil to generate a gradient field. The method further includes distortion-correcting the reconstruction image. The method further includes back-transforming the distortion-corrected reconstruction image, by an image processing device, into a distortion-uncorrected reconstruction image, the back-transforming uses a first algorithm or a second algorithm including a second input value associated with the measurement signal, the second input value being a fictitious gradient field value associated with a distorted measuring point at which the measurement signal is processed, and the second input value is raised or lowered by a nonlinear field component of the real gradient field compared with a linear ideal gradient field.

PRIORITY STATEMENT

This application is the national phase under 35 U.S.C. §371 of PCTInternational Application No. PCT/EP2006/064212 which has anInternational filing date of Jul. 13, 2006, which designated the UnitedStates of America and which claims priority on German Patent ApplicationDE 10 2005 034 648.0 filed Jul. 25, 2005, the entire contents of whichare hereby incorporated herein by reference.

FIELD

At least one embodiment of the invention relates to a method forprocessing a 2D or 3D reconstruction image that is recorded by amagnetic resonance device. For example, it may relate to one comprisinga gradient coil that generates a gradient field, and isdistortion-corrected with regard to a given nonlinearity—leading to animage distortion—of the gradient field by using an algorithm thatprocesses the measurement signals at various measuring points lying inthe imaging volume, which algorithm processes, with respect to eachsignal processed by it, a first input value describing the real gradientfield given at the real measuring point of the signal.

BACKGROUND

A magnetic resonance device serves for recording or generating images ofan examination object that are acquired by the signals resulting from aradio frequency excitation and in which the image is subsequentlydetermined or reconstructed. To this end, a basic field magnet is usedto generate a basic field that is as homogeneous as possible and has ahomogeneity volume of defined homogeneity. Superposed on the field forimaging purposes is a gradient field generated by way of a gradient coiland having field components in the x-, y- and z-directions. Finally, aradio frequency coil produces an RF pulse for the spin excitation thatleads to the signal generation. The design and mode of operation of amagnetic resonance device are adequately known to the person skilled inthe art and require no further explanation.

The recording of a magnetic resonance image or a tomogram is preferablyperformed at the center of the approximately spherical homogeneityvolume, the so-called isocenter. In the context of a so-called“isocentering” concept recently introduced, the slice set to be measuredis positioned at the isocenter by automatic table displacement for eachprotocol used for a measurement, that is to say a signal recording forimaging. That is to say; for each slice to be recorded the patient isreadjusted as necessary such that the body region in which the slicelies is positioned at the isocenter. This ensures the best possiblebasic field homogeneity and gradient linearity, and thus image quality,for the volume to be imaged.

In order to avoid systematic errors during the slice planning, that isto say the definition of the slices to be recorded, the slice planningmay be done in the context of the isocentering concept exclusively ondistortion-corrected images. Such images are corrected by geometricdistortions that result from gradient nonlinearities. When constructinga magnetic resonance image using one or more algorithms starting fromthe recorded measurement signals, it is firstly assumed that there is anideal linear gradient field.

However, real gradient fields deviate from this idealized linear profileand have nonlinear components. This additional nonlinearity has theconsequence that a signal measured at a first real location falselyappears at a second, other location after the reconstruction. Via theso-called distortion correction, these errors are corrected on the basisof knowledge of the spatial nonlinearity of the gradient fields with theaid of the algorithm or algorithms used, which have correspondingcorrection sections. Since these distortion-corrected imagesconsequently exhibit images that are geometrically or anatomicallycorrect, the aim is to apply the distortion correction to all measuredimages.

Since specific applications such as, for example, spectroscopy,necessarily dictate the use of undistorted images in order to ensure anabsolute positioning accuracy of protocol planning and of imagingevaluation, it is not the processed, distortion-corrected images or datarecords that are filed, but the originally measured data records thatexhibit the distortions owing to the nonlinearities. Storing both theoriginally recorded image data records, that is to say the distorted 2Dor 3D reconstruction images, as well as the distortion-correctedreconstruction images in the image database is not an option, since thisdoubles the image data volume to be stored.

Consequently, evaluating images in the context of slice planning, whichin by far most cases is performed with the aid of thedistortion-corrected images, always requires these images to berecalculated from the original measured data. Thus, in a normaloperation there is consequently a need for considerable and timeconsuming computer performance resulting from the requirement that theundistorted image data be on hand for a few applications.

SUMMARY

At least one embodiment of the invention involves a problem ofspecifying a method that is improved by comparison.

Provided for the purpose of a solution is a 2D or 3D reconstructionimage processing method in which method the distortion-correctedreconstruction image is back transformed into a distortion-uncorrectedreconstruction image by using the first algorithm or a second algorithmcorresponding thereto and to which there is given as second input valuein relation to each signal processed by it one such as describes afictitious gradient field at the respective distorted measuring point atwhich the processed signal appears, and is raised or lowered by thenonlinear field component of the real gradient field compared with thelinear ideal gradient field.

At least one embodiment of the invention involves an idea of an inversedistortion correction in the context of which use is made of thealgorithm, or of an algorithm normally used for distortion correctionbut which is given only another input value that describes the gradientfield. This input value describes a “fictitious” or “effective” gradientfield that describes the back transformation, and thus consequentlyimages the nonlinear field component, as considered in the context ofthe distortion correction, with back transformation or inversely. Atransformation, induced by distortion correction, of the actuallyrecorded measurement signal from the distortion-induced measuring pointto the real measuring point is thereby cancelled or inverted, that is tosay the signals of the distortion-corrected image, which appear at thereal measuring points as a consequence of the correction, are imagedback to the distortion-induced “wrong” measuring point.

The inventive method of at least one embodiment thus permits exclusivelythe distortion-corrected 2D or 3D image data records or reconstructionimages to be filed in the image data memory. These are generally usedduring operation. However, should it be necessary for the purpose ofslice planning etc. to have to make recourse to an original image, it ispossible when applying the inventive method to invert the distortioncorrection in a simple way and to use the distortion-correctedreconstruction image to determine the originally recordeddistortion-uncorrected reconstruction image. In at least one embodiment,it is preferred to this end to use the same algorithm that was used forthe distortion correction, all that is required is to determine andprovide another input value in order to undertake the inversecorrection, and so the inventive back transformation can also beperformed very easily.

As set forth above, the central “element” of the inverse correctionmethod is the respective input value specific to pixel or measuringpoint. In the context both of the distortion correction and of the backtransformation, for performance reasons it is not usual to process allpixels or signals at all measuring points. However, only a set ofsignals or measuring points between which interpolation is then carriedout. If very high image qualities are desired, however, it is alsopossible to process every pixel or every signal.

In at least one embodiment, it is preferred to undertake the followingsteps in order to determine the pixel-specific second input value:

determination of the respective nonlinear field component at each realmeasuring point of a processed signal of the distortion-corrected 2D or3D reconstruction image in each of the two or three spatial directions,

determination of the geometrical distortion in the three spatialdirections, and determination of the position of the respectivedistorted measuring points,

and determination of the second input value with the aid of therespective nonlinear field component and of the field component of thelinear ideal gradient field at the distorted measuring point.

In the context of the first method step, there is determined in relationto each measuring point in the distortion-corrected 2D or 3Dreconstruction image by comparison with the ideal linear gradient fieldthat nonlinear field component which is given at this point between thereal gradient field, which is generated at this point, and the idealgradient field. Subsequently, the value of the real, nonlinear gradientfield at the real, distortion-corrected measuring point is used todetermine the corresponding magnetic field value on the linear gradientfield curve and the associated distorted measuring point, that is to saythe distortion is determined in each of the three spatial directions foreach measuring point in the distortion-corrected image. Subsequently thesecond input value is determined, which results from the value of thefield component of the linear ideal gradient field at the distortedmeasuring point (which corresponds to the value of the real fieldcomponent at the actual measuring point) and from the nonlinear fieldcomponent. This “effective gradient field value” at the respectivedistorted measuring point is subsequently used as a basis for the backtransformation, and applied to the signal at the respective associatedreal, distortion-corrected measuring point. This mode of procedure isundertaken with reference to all two or three spatial directions. Thedetermination of this “effective” or “fictitious” gradient field valueor gradient field from the known real, nonlinear gradient field and theideal, linear gradient field is extremely simple and can be performedvery quickly.

In at least one embodiment, it is preferred to use as first or as secondalgorithm of one such as is given development coefficients of amultipole development of the gradient field, the developmentcoefficients being determined with the aid of the second input values. Aknown way of correcting distortion is the so-called multipoledevelopment of the gradient field, which is a spherical functiondevelopment in which the field is represented as the sum of variousterms. In the context of this development, use is made of developmentcoefficients a and b that describe the respective nonlinearity at therespective point being considered. These development coefficients can bedetermined by using such a distortion correction algorithm with the aidof the fictitious or effective gradient field as previously described.The person skilled in the art is sufficiently well aware of themultipole development or the distortion correction with the use ofdevelopment coefficients of a multipole development, and so there is noneed to go into this in more detail.

In addition to the method itself, at least one embodiment of theinvention further relates to a magnetic resonance device comprising animage processing device for processing measured signals and for imagereconstruction, designed for carrying out the above-described method.

BRIEF DESCRIPTION OF THE DRAWINGS

Further advantages, features and details of the invention emerge fromthe example embodiment described below, as well as with the aid of thedrawings, in which:

FIG. 1 shows a schematic illustration of a magnetic resonance device and

FIG. 2 shows a diagram illustrating the determination of the fictitiousor effective gradient field.

DETAILED DESCRIPTION OF THE EXAMPLE EMBODIMENTS

FIG. 1 shows an inventive magnetic resonance device 1 including thesignal recording section 2, which includes the basic field magnet (notshown in more detail), a gradient coil 3 and a radio frequency coil (notshown in more detail) as well as the conventional further components,for which there is no need to give more detail. The magnet generates inthe known manner a basic field with a homogeneity volume that ishomogenized by using suitable shim devices such as, for example, ironshim plates or shim coils. These shim devices are likewise notillustrated in more detail, since they are sufficiently well known tothe person skilled in the art. The gradient coil 3 is used to generatein a known way a gradient field that has three field components pointingin the respective spatial directions x, y, z and really exhibits acertain nonlinearity.

Further shown is a control device 4 that controls the general operationof the system and thus also the image recording, and exhibits an imageprocessing device 5 and an assigned image data memory 6 as well as anassigned monitor 7 for displaying the 3D reconstruction images generatedvia the image processing device 5. The imaging signals, which arereceived via the suitable signal recording devices or antennas in therecording section 2 and are processed in the image processing device 5are given to the control device 4. The image processing device 5 isdesigned for the 3D reconstruction and for correcting the imagedistortion resulting from the nonlinearities of the gradient field. Atleast one or, if appropriate, a number of reconstruction or correctionalgorithms are stored to this end. A person skilled in the art issufficiently well aware of different reconstruction or correctionalgorithms.

In the case of the inventive magnetic resonance device of an embodimentof the present application, the image data memory 6 stores thedistortion-corrected image data records or reconstruction images, butnot the image data records or signal sets really recorded. If, insteadof a distortion-corrected image, it is now necessary to output on themonitor 7 an originally recorded uncorrected image, the image processingdevice 5 is used to access the respective image data record in the imagedata memory 6 and undertake a back transformation of the image data,that is to say image data are determined as they were originallyrecorded. The 2D or 3D reconstruction image is then determinedtherewith.

Descriptions are given below of, on the one hand, the principle of thedistortion correction and, on the other hand, the inventive principle ofthe inverse distortion correction for enabling the inventive backtransformation.

Magnetic resonance imaging is based on the time-dependent measurement ofthe magnetic resonance signals in conjunction with the application of amagnetic field gradient. When the reconstructing images are using themeasured signals, it is assumed that these gradients exhibit exclusivelylinear terms. The corresponding relationships are explained below by wayof example for the x-axis, in order to simplify the illustration. Ofcourse, corresponding statements are also valid with reference to the y-and z-axes.

The ideal magnetic field B_(i)(x) is given as a function of the point xbyB _(i)(x)=G·x,G being a constant value specifying the gradient strength.

However, real gradient fields with finitely extended coil geometriesalso exhibit nonlinearities that lead to spatial distortion of thereconstructed images.

This deviation of the real fields B_(r)(x) from the idealized profilecan be represented as follows:B _(r)(x)=B _(i)(x)+ΔB _(r)(x)=G·x+ΔB _(r)(x),ΔB_(r)(x) describing the nonlinear field component, (here in thex-direction). The consequence of this additional nonlinear fieldcomponent is that a measured signal from the point x_(t), that is to saythe real measuring point, appears falsely at the point x_(m) after thereconstruction. The following then applies for the true point x_(t):

$x_{t} = {x_{m} + \frac{\Delta\;{B_{r}\left( x_{t} \right)}}{G}}$

Existing algorithms for distortion correction are based on the knowledgeof this spatial nonlinearity ΔB_(r)(x) of the gradient fields. Thisnonlinearity is a system property and is typically parameterized as acoefficient of a multipole development.

The inventive method of at least one embodiment now offers a simplepossibility for the back transformation of the distortion-correctedimages into the associated distortion-uncorrected image by usingexisting methods or algorithms of the “normal” distortion correction.The sole difference is the use of a so-called “effective” or“fictitious” gradient field that describes the back transformation. Thisgradient field B_(e)(x) can be described asB _(e)(x)=G·x−ΔB _(e)(x),ΔB_(e)(x) being a nonlinear component of the “effective” gradient field.Consequently, in complete analogy with the above equation, this“effective” gradient field must calculate x_(m) in accordance with

${x_{m} = {x_{t} + \frac{\Delta\;{B_{e}\left( x_{m} \right)}}{G}}},$the nonlinear component of the effective gradient field being determinedin accordance withΔB _(e)(x _(m))=ΔB _(r)(x _(t)).

These relationships emerge clearly from FIG. 2, where the point x isplotted along the abscissa, and the field strength B of the gradientfield is plotted along the ordinate. Shown firstly is the dashed linewhich describes the ideal linear gradient field B_(i)(x)=G·x. Furthershown, via the curve B_(r)(x), is the real gradient field profile, andalso an example of the “effective” gradient field B_(e)(x).

The first step in calculating the “effective” gradient field at a pointthat is to be back transformed in the context of the inverse distortioncorrection is to determine at the real, distortion-corrected measuringpoint x_(t) the nonlinear field component ΔB_(r)(x_(t)) that resultsfrom the difference between the ideal gradient field ΔB_(i)(x_(t)) atthe point x_(t) and the real gradient field B_(r)(x_(t)). Subsequently,the field value that corresponds to the real gradient field valueB_(r)(x_(t)) at the point x_(t) is determined on the ideal gradientfield curve B_(i)(x). As can be seen from FIG. 2, the distortedmeasuring point x_(m) results therefrom.

In order to determine the effective gradient field value at the pointx_(m), the value is now determined asB_(e)(x_(m))=G·x_(m)−ΔB_(r)(x_(t)). That is to say, the gradient fieldvalue on the ideal field curve is raised or lowered by this valuedepending on the sign of the nonlinear field component of the realgradient field at the point x_(t). The effective nonlinearityΔB_(e)(x_(m)) thus corresponds to the effective real nonlinearityΔB_(r)(x_(t)).

Starting by way of example only along the x-axis, this calculation isnow carried out for a family of points x_(t) ^(i), which is to say thatthe respective distortion Δx^(i)=ΔB(x_(t) ^(i))/G is calculated for thisfamily of points.

Subsequently, the effective gradient field is determined as B_(e)(x_(m)^(i))=G·x_(m) ^(i)−ΔB_(r)(x_(t) ^(i)) at the respective point x_(m)^(i)=x_(t) ^(i)+Δx^(i). These magnetic field values at the points x_(m)^(i) then serve as input values for the distortion correction methodbeing used, that is to say the correction algorithm being used, bywhich, for example, the distortion correction has already been performedin the context of the first processing.

If the distortion correction method has to be provided with developmentcoefficients of a multipole development of the field, said developmentcoefficients can, as already described, be determined from the magneticfield values B_(e)(x_(m) ^(i)) at the points x_(m) ^(i).

Finally, it may be pointed out once again that the above-describeddetermination of the effective gradient field in all three spatialdirections is carried out for each point of a family of points x_(t)^(i), y_(t) ^(i), z_(t) ^(i) when a 3D reconstruction image is present;of course, only the two relevant spatial directions are considered inthe case of a 2D reconstruction image.

Example embodiments being thus described, it will be obvious that thesame may be varied in many ways. Such variations are not to be regardedas a departure from the spirit and scope of the present invention, andall such modifications as would be obvious to one skilled in the art areintended to be included within the scope of the following claims.

1. A method for processing a reconstruction image, the methodcomprising: recording the reconstruction image by a magnetic resonancedevice having a gradient coil to generate a gradient field;distortion-correcting the reconstruction image by an image processingdevice, the distortion correcting being with regard to a nonlinearity,the distortion correcting resulting in an image distortion of thegradient field, the distortion correcting uses a first algorithmconfigured to process a measurement signal at various measuring pointsof a plurality of measuring points lying in an imaging volume, the firstalgorithm including a first input value describing a real gradient fieldgiven at a real measuring point of the plurality of real measuringpoints of the measurement signal; back-transforming thedistortion-corrected reconstruction image, by the image processingdevice, into a distortion-uncorrected reconstruction image, theback-transforming uses a second algorithm corresponding to the firstalgorithm, the second algorithm including a second input valueassociated with the measurement signal, the second input value being afictitious gradient field value associated with a distorted measuringpoint at which the measurement signal is processed, and the second inputvalue is one of raised and lowered by a nonlinear field component of thereal gradient field compared with a linear ideal gradient field.
 2. Themethod as claimed in claim 1, further comprising: determining thenonlinear field component at each real measuring point of the pluralityof measurement points of the distortion-corrected reconstruction imagein each spatial directions of the distortion-corrected reconstructionimage; determining a geometrical distortion in each of the spatialdirections of the distortion-corrected reconstruction image; determininga position of the distorted geometrical measuring points; anddetermining the second input value using the nonlinear field componentand a field component of the linear ideal gradient field at thedistorted measuring point.
 3. The method as claimed in claim 1, furthercomprising: determining development coefficients of a multipoledevelopment of the gradient field using at least one of the first andsecond algorithm, wherein the development coefficients are determinedbased on the second input value.
 4. The method of claim 1, wherein thereconstruction image is one of a two dimensional image and a threedimensional image.
 5. A magnetic resonance device, comprising: an imageprocessing device configured to, process measured signals, reconstructimages from the measured signals, and back-transform adistortion-corrected reconstruction image into a distortion-uncorrectedreconstruction image using a second algorithm corresponding to the firstalgorithm, the second algorithm having an input value in relation toeach signal processed by the second algorithm, the input value being afictitious gradient field at a distorted measuring point associated withthe processed signal, the input value is one of raised and lowered by anonlinear field component of a real gradient field compared with alinear ideal gradient field.
 6. The method as claimed in claim 5,further comprising: determining development coefficients of a multipoledevelopment of the gradient field using at least one of the first andsecond algorithm, wherein the development coefficients are determinedbased on the input value.